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[quote=Anonymous][quote=Anonymous][quote=Anonymous]Memorization does not come at the expense of understanding. They are not mutually exclusive .[/quote]

I don't think the teacher is saying that they are.  But instead that the order of learning matters.  A kid who learns to memorize early may not put the effort into learning the multiplication concepts thoroughly. [b] And instead, s/he may just use the memorized algorithms to solve the problems.[/b]   I can see my son doing that.  He's working on three digit addition right now in third grade, and they are using the partial sums method of solving them, rather than carrying digits to the left.   This method really instills place value for him, in a way just carrying a digit to a different column does not.  He will learn that traditional algorithm, too, but if he had known it first, he probably wouldn't do the work involved with the partial sums method.  Because this algorithm feels unwieldy, too lengthy, yet it teaches the concept very thoroughly.[/quote]

The schools really don't give kids the opportunity to do that.  Even if the facts are memorized, for years they are required to "show their strategies"  in their work by skip counting, repeated addition, arrays, etc.  Honestly the vast majority of students get these concepts pretty quickly, and having to do these long drawn-out processes for years after it's already understood it tortuous. [/quote]

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